1. Tardigrade
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  4. Two spherical conductors A and B of radii R and 2R respectively, are separated by a large distance. If some charge is given to both the spheres and later they are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

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Q. Two spherical conductors $A$ and $B$ of radii $R$ and $2R$ respectively, are separated by a large distance. If some charge is given to both the spheres and later they are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

When the spherical conductors are connected by a conducting wire, charge is redistributed and the spheres attain a common potential $V$ .
$\therefore $ Intensity $\text{E}_{\text{A}}=\frac{1}{4 \pi ε_{0}}\frac{\text{Q}_{\text{A}}}{\text{R}_{\text{A}}^{2}}$
or or $\quad E_A=\frac{1 \times C_A V}{4 \pi \varepsilon_0 R_A^2}=\frac{\left(4 \pi \varepsilon_0 R_A\right) V}{4 \pi \varepsilon_0 R_A^2}=\frac{V}{R_A}$
Similarly $\text{E}_{\text{B}}=\frac{\text{V}}{\text{R}_{\text{B}}}$
$\therefore $ $\frac{\text{E}_{\text{A}}}{\text{E}_{\text{B}}}=\frac{\text{R}_{\text{B}}}{\text{R}_{\text{A}}}=\frac{2}{1}$ .